The PascGalois Project: Visualization in Abstract Mathematics

索尔兹伯里大学与加州州立大学弗雷斯诺、洪堡州立大学、肯尼索州立大学、佛罗里达新学院和爱丁堡州立大学合作，正在开发在线材料，以加强几门数学课程，包括为未来教师提供的课程。学生们经常发现抽象的数学很难形象化。他们很少看到课程和独立数学探究之间的联系。PascGalois项目提供了一类有趣的离散动力系统，这些系统是在代数结构上生成的，例如群，以及这些系统的彩色图形表示，让学生看到与动力学交织在一起的代数和数论性质。这个项目的主要目标是：开发在线活动，包括Java小程序，为抽象代数，离散数学，数论，动力系统和计算机图形学;培养学生对困难数学概念的直观和直观的理解;为未来的数学教师建立有效使用技术的模型，并为他们实施NCTM标准做好更好的准备;在上层建筑之间架起一座桥梁，通过提供一个有趣的和可访问的研究项目的来源。该项目的智力价值是在创新活动设计的高层次的数学课程，揭示课程之间的联系，否则可能会出现无关，并产生本科生的研究项目。两个夏季PascGalois务虚会突出了本科生的研究工作。更广泛的影响来自Java小程序的在线传播和通过MathDL等场所的活动。这些活动将被纳入整个数学课程。

Salisbury University, in collaboration with California State University Fresno, Humbolt State University, Kennesaw State University, New College of Florida, and Pittsburg State University, is developing online materials to enhance several mathematics courses, including those for prospective teachers. Students frequently find abstract mathematics difficult to visualize. They rarely see links between coursework and independent mathematical inquiry. The PascGalois Project provides an interesting class of discrete dynamical systems generated over algebraic structures, such as groups, and color graphical representations of these systems that allow students to see algebraic and number theoretic properties intertwined with the dynamics.The primary objectives of this project are to: develop online activities including Java applets that provide a visual component for courses including abstract algebra, discrete mathematics, number theory, dynamical systems, and computer graphics; develop students' visual and intuitive understanding of difficult mathematical concepts; model effective use of technology for prospective mathematics teachers and better prepare them to implement the NCTM standards; and create a bridge between upper-level courses and undergraduate research by providing a source of interesting and accessible research projects.The intellectual merit of the project is in the innovative activities designed for upper-level mathematics courses, revealing connections between courses that otherwise may appear unrelated, and the undergraduate research projects that are generated. Two summer PascGalois retreats highlight the undergraduate research efforts.Broader impacts follow from online dissemination of the Java applets and activities through a venue such as MathDL. These activities will be integrated throughout the mathematics curriculum.